Match each polynomial on the left with its two factors on the right.

9514 1404 393

Answer:

  (b)  BC = B"C"/3

Step-by-step explanation:

Choices A, C, D are all different ways of expressing the same relationship, and they are all incorrect.

B"C" is segment BC after dilation by a factor of 3, so it is 3 times as long as BC. That is, BC is 1/3 the length of B"C", choice B.

Answer:

1.5 cubic metres

Step-by-step explanation:

Given that in a concrete mix, cement makes up 1 part, sand makes up 2 parts and gravel makes up 3 parts.

The total number of parts = 1 + 2 + 3 = 6 parts.

The amount of marvel present the concrete mix = amount of marvel / total mix

= 3 parts / 6 parts = 1/2

Since 3 cubic metres of concrete is enough for the path, hence the amount of gravel needed is:

Amount of gravel = 1/2 * 3 cubic metres of concrete = 1.5 cubic metres

Answer:

ON = KJ

Step-by-step explanation:

JKL = NOP

We know the angles match

<J = <N

<K = <O

< L = <P

And we know

JK = NO

KL =  OP

JL = NP

We are looking for ON = KJ

9514 1404 393

Answer:

  (d)  KJ

Step-by-step explanation:

The segment of interest is named using the 2nd and 1st letters of the right side of the similarity statement.

The corresponding segment will be named using the 2nd and 1st letters of the left side of the similarity statement: KJ.

Answer:

Step-by-step explanation:

You need to put parentheses around the radicands.

√z · √(30z²) · √(35z³) = √(z·30z²·35z³)

= √(1050z⁶)

= √(5²·42z⁶)

= √5²√z⁶√42

= 25z³√42

The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have been the expression as:

⇒ √z · √(30z²) · √(35z³)

Multiply and remove all perfect squares from inside the square roots

⇒ √(z·30z²·35z³)

⇒ √(1050z⁶)

⇒ √(5²·42z⁶)

Assume z is positive.

⇒ √5²√z⁶√42

⇒ 25z³√42

Therefore, the obtained expression would be 25z³√42.

Learn more about Arithmetic operations here:

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Answer:

below

Step-by-step explanation:

hope it is well understood?

The slope is 4 and y- intercept is 13

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

A slope exists Numerical calculation of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment stands as the proportion of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

Given

Slope

y = 4x-3

dy/dx = 4

slope =  4

intercepts y = 4(4) 3

y = 16-3

y = 13

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Answer:

Point estimate = 76.4

Margin of Error = 2.680

Step-by-step explanation:

Given that distribution is approximately normal;

The point estimate = sample mean, xbar = 76.4

The margin of error = Zcritical * s/√n

Tcritical at 95%, df = 42 - 1 = 41

Tcritical(0.05, 41) = 2.0195

Margin of Error = 2.0195 * (8.6/√42)

Margin of Error = 2.0195 * 1.327

Margin of Error = 2.67989

Margin of Error = 2.680

Answer:

A. Increase speed to approximately 7.1 mph so that you cover the field more.

Step-by-step explanation:

The soil samples for the next field require more fertilizer coverage therefore there is need for more field coverage by the equipment. The speed of the tractor will be increase to 7.1 mph so that greater area can be covered in lesser time.

9514 1404 393

Answer:

Step-by-step explanation:

We observe that the second equation of System B has had the x-term eliminated. That can be accomplished by adding 3 times the first equation to the second.

"To get System B, the second equation in System A was replaced by the sum of that equation and 3 times the first equation. The solution is the same as the solution to System A."

9514 1404 393

Answer:

  120

Step-by-step explanation:

I find it pretty easy to obtain the solution by graphing ...

  c(x) -13865 = 0

The positive value of x that makes this so is x = 120.

120 units will have a cost of 13,865 to manufacture.

__

If you like to solve this algebraically, you can probably do it most easily by completing the square.

  x^2 -5x = -65 +13865

  x^2 -5x +6.25 = 13806.25 . . . . . add the square of (-5/2)

  (x -2.5)² = 13806.25

  x -2.5 = √13806.25 = 117.5 . . . . only the positive square root is interesting

  x = 117.5 +2.5 = 120

9514 1404 393

Answer:

  [tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]

Step-by-step explanation:

It's pretty straightforward. You want ...

  f(x) - g(x)

Substituting the given function definitions gives ...

  [tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]

Answer:

a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches

The sampling distribution of the sample means annual rainfall for California is 1.278.

b)

[tex]E(\bar x) = \mu_{2} = 42[/tex] inches

The sampling distribution of the sample means annual rainfall for New York is 1.0435.

c)

Here, The standard error of New York is smaller because the sample size is larger than for California.

Step-by-step explanation:

California:

[tex]\mu_{1} = 22[/tex] inches.

[tex]\sigma_{1}[/tex] = 7 inches.

[tex]n_{1}[/tex] = 30 years.

New York:

[tex]\mu_{2} = 42[/tex] inches.

[tex]\sigma_{2}[/tex] = 7 inches.

[tex]n_{2}[/tex] = 45 years.

a)

[tex]E(\bar x) = \mu_{1} = 22[/tex] inches

[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]

b)

[tex]E(\bar x) = \mu_{2} = 42[/tex] inches

[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]

c)

Here, The standard error of New York is smaller because the sample size is larger than for California.

Answer:

Step-by-step explanation:

From the given information:

We can see that:

[tex]x + 2y + 3z = 0 --- (1) \\ \\ 2x + 4y + 6z = 0 --- (2)[/tex]

From equation (1), if we multiply it by 2, we will get what we have in equation (2).

It implies that,

x + 2y + 3z = 0    ⇔   2x + 4y + 6z = 0

And, W satisfies the equation x + 2y + 3z = 0

i.e.

W = {(x,y,z) ∈ R³║x+2y+3z = 0}

Now, to determine the distance through the plane W and point is;

[tex]y = [1 \ 1 \ 1]^T[/tex]

Here, the normal vector [tex]n = [1\ 2\ 3]^T[/tex] is related to the plane x + 2y + 3z = 0

Suppose θ is the angle between the plane W and the point [tex]y = [1 \ 1 \ 1]^T[/tex], then the distance is can be expressed as:

[tex]||y|cos \theta| = \dfrac{n*y}{|n|}[/tex]

[tex]||y|cos \theta| = \dfrac{[1 \ 2\ 3 ]^T [1 \ 1 \ 1] ^T}{\sqrt{1^2+2^2+3^2}}[/tex]

[tex]||y|cos \theta| = \dfrac{[1+ 2+ 3 ]}{\sqrt{1+4+9}}[/tex]

[tex]||y|cos \theta| = \dfrac{6}{\sqrt{14}}[/tex]

[tex]||y|cos \theta| = 3\sqrt{\dfrac{2}{7}}[/tex]

Answer:

Four places to the left.

Step-by-step explanation:

14.6/10000

=> 1.46/1000 [Shifted 1 decimal place after dividing by 10]

=> 0.146/100 [Shifted 1 decimal place after dividing by 10]

=> 0.0146/10 [Shifted 1 decimal place after dividing by 10]

=> 0.00146   [Shifted 1 decimal place after dividing by 10]

Number of decimal places = 1+1+1+1=4

Four places to the left.

Answer:

3/5 so A.

Step-by-step explanation:

Answer:

slope = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (1, 5)

m = [tex]\frac{5-2}{1-(-4)}[/tex] = [tex]\frac{3}{1+4}[/tex] = [tex]\frac{3}{5}[/tex]

1. Move terms to the left side

2.Subtract the numbers

3.Use the quadratic formula

4.Simplify

5.Separate the equations

6.Solve

Rearrange and isolate the variable to find each solution.

Solution,

Solution

x=5±√39

Answer:

10.6

Step-by-step explanation:

A simple sketch of the question would give a right angled triangle. So that we can easily apply the Pythagoras theorem to determine the length of the cable required.

Let the length of the cable required be represented by x.

[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]7^{2}[/tex]

   = 64 + 49

[tex]x^{2}[/tex] = 113

x = [tex]\sqrt{113}[/tex]

  = 10.63

x = 10.6

The length of the cable required is 10.6 in feet.

The length of the cable needed to support the tenth wall is approximately 10.6 ft.

The situation forms a right angle triangle.

Right angle triangle has one of it side as 90 degrees.

Therefore,

The tent wall is the opposite side of the triangle.

The table feet from the base of the tent is the adjacent side of the triangle.

Using Pythagoras's theorem the cable needed can be found.

Therefore,

c² = 64 + 49

c = √113

c = 10.6301458127

length of the cable ≈ 10.6 feet

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Hello!

f(g(x)) = 4 - 2 × (3x²) <=>

<=> f(g(x)) = 4 - 6x²

Answer: B. f(g(x)) = 4 - 6x²

Good luck! :)

Let we find the composition,

→ f(g(x)) = 4 (-2 × 3x²)

→ f(g(x)) = 4 -6x²

Hence, option (B) is the answer.

Answer:

5

Step-by-step explanation:

the only point in the chart, which has x=0 as coordinate, is the point up there at y=5.

and that is automatically the result. there is not anything else to it.

Answer:

Each triangle is a right triangle.

Step-by-step explanation:

You can see each one has one 90 degree corner.

Answer:

13. True

14. True

15. False

Step-by-step explanation:

By using the Pythagorean Theorem a^2+b^2=c^2, you can evaluate whether or not the triangles are right triangles.

13. 8^2+15^2=17^2   ->  64+225=289  -> TRUE

14. 50^2+120^2=130^2  -> 2500+14400=16900  -> TRUE

15. 12^2+35^2=36^2  -> 144+1225 =/=1296 -> FALSE

Answer:

b. 01285 esa es, espero este buena y que te ayude

Answer:

Step-by-step explanation:

This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.

We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is

[tex]A=lw[/tex]. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:

[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex] . If our unknown is the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:

The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our [tex]\frac{dl}{dt}[/tex];

the width is increasing at a rate of 6 cm/s, so that satisfies our [tex]\frac{dw}{dt}[/tex];

and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:

[tex]\frac{dA}{dt}=12(6)+8(7)[/tex] and

[tex]\frac{dA}{dt}=72+56[/tex] so

[tex]\frac{dA}{dt}=128\frac{cm^2}{s}[/tex]

Answer:

3x³+3x²+3x+8+[tex]\frac{4}{x-1}[/tex]

Step-by-step explanation:

You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.

Answer:

g(x)=x-3

Problem:

If f(x+3)=x+6 find inverse of function f(x).

Step-by-step explanation:

Let u=x+3, then x=u-3.

Make this substitution into our given:

f(u)=(u-3)+6

Simplify:

f(u)=u+(-3+6)

f(u)=u+3

Now let's find the inverse of f(u)...

Or if you prefer rename the variable...

f(x)=x+3

Now, we are going to solve y=x+3 for x.

Subtracting 3 on both sides gives: y-3=x.

Interchange x and y: x-3=y.

So the inverse of f(x)=x+3 is g(x)=x-3.

Answer:

The answer is g(x)=x-3

Step-by-step explanation:

If f(x+3)=x+6 find inverse of function f(x).

Let u=x+3, then x=u-3.

Make this substitution into our given:

f(u)=(u-3)+6

Simplify:

f(u)=u+(-3+6)

f(u)=u+3

Now let's find the inverse of f(u)...

Or if you prefer rename the variable...

f(x)=x+3

Now, we are going to solve y=x+3 for x.

Subtracting 3 on both sides gives: y-3=x.

Interchange x and y: x-3=y.

So the inverse of f(x)=x+3 is g(x)=x-3.

Answer:

7 1/2

Step-by-step explanation:

2 1/2 ÷ 1/3

Change to an improper fraction

(2*1+2)/2 ÷ 1/3

5/2 ÷1/3

Copy dot flip

5/2 * 3/1

15/2

Change to a mixed number

7 1/2

Answer:

0.19

Step-by-step explanation:

Jane bought a shoe for 54.82 euros

She gave the store owner 55 euros

= 55-54.82

= 0.18 euros to franc

= 0.18× 1.08222

= 0.19 franc

Answer:

Statement A is correct

Step-by-step explanation:

Statement A is correct:  Model A1 (0.25) is more prefered than Model C3 (0.15)

Answer: He can make 36 different salds

Step-by-step explanation:

Answer:

7.3

Step-by-step explanation:

y=2.5x+5.8

=2.5×0.6+5.8

= 1.5+.8

=7.3